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The Schulze voting method aggregates voter preference data using maxmin-weight graph paths, achieving the Condorcet property that a candidate who would win every head-to-head contest will also win the overall election. Once the voter…

Data Structures and Algorithms · Computer Science 2024-12-02 Arushi Arora , David Eppstein , Randy Le Huynh

Schulze's rule is used in the elections of a large number of organizations including Wikimedia and Debian. Part of the reason for its popularity is the large number of axiomatic properties, like monotonicity and Condorcet consistency, which…

Artificial Intelligence · Computer Science 2013-04-04 Serge Gaspers , Thomas Kalinowski , Nina Narodytska , Toby Walsh

We propose a new single-winner election method ("Schulze method") and prove that it satisfies many academic criteria (e.g. monotonicity, reversal symmetry, resolvability, independence of clones, Condorcet criterion, k-consistency,…

Computer Science and Game Theory · Computer Science 2025-10-28 Markus Schulze

We study computational aspects of a well-known single-winner voting rule called the Schulze method [Schulze, 2003] which is used broadly in practice. In this method the voters give (weak) ordinal preference ballots which are used to define…

Data Structures and Algorithms · Computer Science 2021-06-25 Krzysztof Sornat , Virginia Vassilevska Williams , Yinzhan Xu

The Schulze method is a voting rule widely used in practice and enjoys many positive axiomatic properties. While it is computable in polynomial time, its straight-forward implementation does not scale well for large elections. In this…

Computer Science and Game Theory · Computer Science 2025-06-19 Theresa Csar , Martin Lackner , Reinhard Pichler

Both Schulze and ranked pairs are voting rules that satisfy many natural, desirable axioms. Many standard types of electoral control (with a chair seeking to change the outcome of an election by interfering with the election structure) have…

Computer Science and Game Theory · Computer Science 2024-05-16 Cynthia Maushagen , David Niclaus , Paul Nüsken , Jörg Rothe , Tessa Seeger

Approval-preferential voting is problematical since it combines two different kinds of information that could by themselves lead to different choices. This article analyses the problem and studies a new proposal to deal with it. The…

Computer Science and Game Theory · Computer Science 2021-01-12 Rosa Camps , Xavier Mora , Laia Saumell

Schulze and ranked-pairs elections have received much attention recently, and the former has quickly become a quite widely used election system. For many cases these systems have been proven resistant to bribery, control, or manipulation,…

Computer Science and Game Theory · Computer Science 2014-06-24 Lane A. Hemaspaandra , Rahman Lavaee , Curtis Menton

Voting theory has become increasingly integrated with computational social choice and multiagent systems. Computational complexity has been extensively used as a shield against manipulation of voting systems, however for several voting…

Computer Science and Game Theory · Computer Science 2011-08-24 Curtis Menton , Preetjot Singh

We prove that the constructive weighted coalitional manipulation problem for the Schulze voting rule can be solved in polynomial time for an unbounded number of candidates and an unbounded number of manipulators.

Computer Science and Game Theory · Computer Science 2020-07-31 Julian Müller , Sven Kosub

Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We…

Computer Science and Game Theory · Computer Science 2013-10-28 Edith Hemaspaandra , Lane A. Hemaspaandra , Joerg Rothe

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the…

Artificial Intelligence · Computer Science 2012-04-20 Andrew Lin

In collective decision making, where a voting rule is used to take a collective decision among a group of agents, manipulation by one or more agents is usually considered negative behavior to be avoided, or at least to be made…

Artificial Intelligence · Computer Science 2013-03-05 Umberto Grandi , Andrea Loreggia , Francesca Rossi , Kristen Brent Venable , Toby Walsh

Much research in electoral control -- one of the most studied form of electoral attacks, in which an entity running an election alters the structure of that election to yield a preferred outcome -- has focused on giving decision complexity…

Computer Science and Game Theory · Computer Science 2026-05-14 Huy Vu Bui , Michael C. Chavrimootoo , Kien T. Le , Son M. Nguyen

Integrity of elections is vital to democratic systems, but it is frequently threatened by malicious actors. The study of algorithmic complexity of the problem of manipulating election outcomes by changing its structural features is known as…

Computer Science and Game Theory · Computer Science 2020-07-21 Andrew Estornell , Sanmay Das , Edith Elkind , Yevgeniy Vorobeychik

Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We…

Computer Science and Game Theory · Computer Science 2015-03-20 Edith Hemaspaandra , Lane A. Hemaspaandra , Joerg Rothe

The Skating System, which originated from the scrutineering system in dance sport tournaments, can be formulated as a voting system: We introduce and formalize the Skating System Single (SkS, for short), a new voting system embedded into…

Computer Science and Game Theory · Computer Science 2025-12-01 Laryssa Horn , Paul Nüsken , Jörg Rothe , Tessa Seeger

Voting is a general method for preference aggregation in multiagent settings, but seminal results have shown that all (nondictatorial) voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where…

Computer Science and Game Theory · Computer Science 2009-09-29 Vincent Conitzer , Tuomas Sandholm

Candidate control of elections is the study of how adding or removing candidates can affect the outcome. However, the traditional study of the complexity of candidate control is in the model in which all candidates and votes are known up…

Computer Science and Game Theory · Computer Science 2016-06-20 Edith Hemaspaandra , Lane A. Hemaspaandra , Joerg Rothe

Election control considers the problem of an adversary who attempts to tamper with a voting process, in order to either ensure that their favored candidate wins (constructive control) or another candidate loses (destructive control). As…

Multiagent Systems · Computer Science 2017-11-27 Bryan Wilder , Yevgeniy Vorobeychik
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